Paper Number

Targeting the Limits of Laser Doppler Vibrometry Martin Johansmann Georg Siegmund Mario Pineda

All Polytec Copyright © 2005

ABSTRACT

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Laser Doppler Vibrometry (LDV) is the workhorse for hard disk drive dynamic testing and has contributed significantly to the development of modern hard disk drives. With increasing areal densities, and component as well as drive miniaturization the performance requirements for laser Doppler vibrometers (LDVs) have continuously grown to confront the demands of increased resolution, bandwidth and accuracy. In this paper we address the limitations of LDV technology and how to get close to those limits. Conventional analog signal processing schemes and modern digital decoding methods are discussed. Examples are given for LDV measurements requiring high resolution digital signal processing and high frequency capability of analog demodulation.

Laser Doppler Vibrometer Principle of Operation

INTRODUCTION One of the first references to LDV design was Drain’s 1975 book “The Laser Doppler Technique” [1]. Subsequently LDVs have become a indispensable tool for the accurate measurement of vibration on small and miniature structures. From these measurements, natural frequencies and mode shapes are extracted and modal parameters like modal mass, stiffness and damping calculated. In early days, LDV measurements were mainly applied to larger structures such as automotive components. Original LDV designs were solely based on bulk optical components. In 1985 [2] and 1988 [2] Lewin presented an improved design incorporating fiber optic light guides. Within a very short time fiber optic based LDVs became the standard tool in the data storage industry and found many different applications in R&D as well as production testing.

The Laser Doppler Vibrometer (LDV) is a non-contact velocity and/or displacement transducer, which is used to measure magnitude and frequency content of large, down to micron size parts. LDVs focus a laser beam on the structure to be tested. The structure scatters or reflects light from the laser beam and the Doppler frequency shift or phase shift of the backscattered light is demodulated to measure the component of velocity / displacement, which lies parallel to the axis of this laser beam. Because of their non-contact nature, LDVs do not massload the structure which is a prerequisite for data storage components, furthermore the natural stiffness and damping of the component is not changed. Laser Vibrometry is a very sensitive optical technique capable of measuring sub-nanometer or even sub-picometer displacements from near DC to several MHz. In addition to their wide frequency range, LDVs have dynamic range not matched by other sensors. This enables measurements that cannot be accomplished by other optical techniques. The Laser Doppler Technique Optical Arrangement For measurements on data storage drives, MEMS and other small structures the low noise level and high resolution of the LDV are of utmost importance in order to detect the smallest vibration levels. In addition to the noise created by signal demodulation electronics, phase noise of the laser contributes to the overall noise of an LDV system. The phase noise corresponds to the line width of the light source.

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The low noise of a single mode HeNe laser, with narrow line widths of in the order of a few millihertz, make it the preferred light source for LDVs. In general, two different optical arrangements for LDV’s have been popular: the homodyne and the heterodyne vibrometer techniques. In a homodyne vibrometer the vibration direction is obtained by processing 2 interference signals (I & Q) which are shifted 90° versus each other. Due to certain disadvantages of the homodyne technique, most commercially available LDVs are now using the superior heterodyne technique. In this the frequency of a reference beam is shifted by an acousto-optic modulator or Bragg cell.

In the heterodyne interferometer as shown in figure 2, an acousto-optic modulator, BC, is incorporated for frequency shifting of the reference beam. The most common shift frequencies are 40MHz and 70MHz. Without any motion (vobject=0) the photo detector will see only the Bragg cell reference frequency ωc With vobject >0 the photo detectors will detect either an increase or decrease in frequency depending on the motion direction of the object. Resolution Limits of Laser Doppler Vibrometry Resolution is a crucial parameter when applying LDVs to data storage component measurements. The main noise sources limiting the LDV resolution are light induced noise (shot noise), thermal noise of detector and preamplifier (Johnson noise), and signal processing noise. The ultimate limiting factor of a LDV is the signalto-noise ratio of the photo detector output. An exact calculation of the LDV resolution is very complex and would extend the scope of this paper. Hence only some basic relationships are given hereafter. A major advantage of coherent light detection by means of an interferometer is the optical amplification of the AC amplitude which can be expressed by the term

Pm Pr Figure 1: Optical arrangements of the classical MachZehnder type interferometer. M is a mirror, BS is a beamsplitter, PBS is a polarizing beamsplitter, L is a laser, QWP is a quarter-wave plate, PD is a photo detector, and T is a telescopic lens array. In the Mach-Zehnder interferometer, as shown in figure 1, the laser beam is divided into 2 beams (measurement and reference beams) utilizing a polarizing beam splitter. A quarter-wave plate rotates the polarization of the backreflected light by the test object by 90° and another beam splitter guides it to the detector. Here the measurement beam and the reference beam are combined. Two photo detectors are used to receive twice the signal power and to remove the DC component.

Pm -Measurement beam power, power

This means doubling the power of the reference beam yields a •2 or 3dB gain for the carrier amplitude (=optical amplification). However the sum power Pm + PY not only generates a DC current, but also shot noise:

ish2 = 2 K ⋅ q ⋅ B (Pm + Pr ) B K q

– detector bandwidth – detector sensitivity factor (A/W) – electron charge

Another noise source is thermal detector/preamplifier combination:

ith2 = k T R

Figure 2: Schematic of the optical arrangement of a heterodyne vibrometer. BC is a Bragg cell

Pr - Reference beam

noise

of

the

4k ⋅ T ⋅ B R – Boltzmann´s constant – absolute temperature – detector load resistance

The reference beam power is usually chosen such that shot-noise power significantly exceeds thermal noise power under given conditions. This point is usually reached at Pr + Pm < 1 mW, depending on bandwidth. The system then is called shot-noise limited and yields the best possible signal-to-noise ratio.

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As shown before, with an appropriate interferometer design, shot noise provides the main contribution to the detector output noise. An LDV system provides displacement information by decoding the phase shift and velocity from the frequency shift (Doppler shift). When looking at the characteristics of the overall noise; it can be shown that phase noise (equivalent to displacement noise) exhibits white noise characteristics, whereas the velocity (FM) noise is proportional to the frequency. This is the reason why velocity noise increases at higher frequency, whereas the displacement noise is constant over frequency. log s 0 -1

Spurious noise peaks, caused mainly by electronic crosstalk, are not higher than 25 pm. The corresponding velocity noise of this system rises from λ/2

the for

is directly related to the displacement of the object

s (tn ) =

λ ϕ (tn ) 4π

Hence by calculating the phase angle a displacement measurement with very high resolution can be achieved. Figure 10: And for small vibration levels s < λ/2

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An arctangent LDV system has been realized on PC platform. The detector signal is converted into the I&Q pair using an analog quadrature demodulator as shown in figure 6. Next, the I&Q signals (plus one reference signal) are digitized by an of-the-shelf A/D board and the signal phase is numerically calculated (figure 7). This system has already been extensively used for measurements on data storage and MEMS components. Not only for measurements on single points but also in conjunction with microscope scanning vibrometer (MSV) systems for full area mapping through a microscope and with dual beam MSV systems for differential measurements. With sufficient number of averages a resolution of less than 1 pm has been achieved bringing us closer to the resolution limit of LDVs as discussed beforehand. A/D Sampling Freq. Max. vibration freq. Max vibration velocity Specified displacement resolution Specified velocity resolution

Laser Doppler Signal Processing utilizing Digital and quasi Real-Time Techniques The LDV concept described before utilizes a PC platform for digitalization of the I&Q signal pair and processing of the phase. Hence a proprietary PC software for data processing and display is always needed and an analog real-time output is not available. Consequently the next development step would be implementing this concept onto a real-time DSP platform without any need for PC hardware. In the arctangent DSP-based LDV the Doppler signal is down mixed to a lower intermediate frequency and digitized by an on-board A/D converter. The I&Q signal pair is created numerically by mixing the signal with a numerical oscillator (NCO). The arctangent calculation provides the phase of the signal. To save calculation time and DSP power the phase is not unwrapped but differentiated in order to achieve velocity values. The velocity data are converted into an analog voltage using a 16 bit D/A converter.

5.12 Msa/s 2 MHz 810 mm/s